Yes. Although birth control pills have a high success rate, they can fail and you can get pregnant while on the pill. Certain factors increase your risk of getting pregnant, even if you're on birth control.
Can you fall pregnant while on the 3 month injection?
If you're using the birth control shot correctly, which means getting it every 12-13 weeks (3 months), it's highly unlikely that you'll get pregnant. Only 6 out of 100 people get pregnant each year while using the shot.
How long does it take to get pregnant if you were preventing?
Most women will get pregnant within six months after stopping birth control. However, in some cases, it can take longer. If you struggle to conceive after birth control, talk to your doctor.